# Power Grid

**Topics:**Electric power transmission, Transmission line, Capacitor

**Pages:**8 (1250 words)

**Published:**January 28, 2013

Faults and Transients on Transmission Lines

Wang Wei weiwan@kth.se 1/12/2011

1. Introduction

Project 1 is about fault currents and transients on transmission lines that may occur due a lightning strike to an overhead line. In this case the transmission line is energized from one side and it’s other side is terminated in a Gas Insulated Substation, see Fig. 1. Several issues will be investigated from this system such as transient overvoltages and short-circuit currents.

Fig.1 Transmission line model

1.1 Given parameters

System voltage Table 1. Basic power line data 420 kV 20 m 13 m 25 cm 25 mm 3800 Ohmm 0.5 m 0.5 m Do = 400 mm, Di = 120 mm

Average height above ground Phase-to-phase distance Triplex conductor, circumscribing diameter Conductor diameter Soil resistivity Tower grounded with metallic hemisphere of radius Generation station neutral grounded with metallic hemisphere of radius Co-axial GIS tube filled with SF6. Outer andd inner diameter

1

2.1 Stationary LLG fault current

A phase-to-phase to ground (LLG) fault occurs in the middle of the line, i.e. YY/2 km from each sub-station. OHL parameters The theory developed by Carson give the approximate expression for the distance to return conductor as a function of the resistivity of the earth and the frequency

D 658

f

658

3800 5736.31m 50

The geometric mean radius is given by

GMR 3 3 0.025 / 2 0.25 / 2 0.0837m

2

1 D 1 5736.31 L11 L22 L33 2 107 ( ln ) 2 107 ( ln ) 2.277 106 H / m 4 GMR 4 0.0837 Z11 Z22 Z33 j 2 fL11 l j 29.69

L12 L21 L23 L32 2 107 ln D 5736.31 2 107 ln 1.218 106 H / m d12 13

Z12 Z21 Z23 Z32 j 2 fL12 l j15.88 L13 L31 2 107 ln D 5736.31 2 107 ln 1.08 106 H / m d13 26

Z13 Z31 j 2 fL13 l j14.08

The impedance matrix can be obtained

j 29.69 Z j15.88 j14.08

j15.88 j 29.69 j15.88

j14.08 j15.88 j 29.69

The capacitance for OHL

2 0 r 2 0 r 9.02 1012 F / m 2H 2 20 ln ln GMR 0.0837 C1 c1 l 9.02 1012 83000 0.5 3.74 107 F c1 GIL parameters

2

L0 2 107 ln c0

Do 2.4 107 H / m Di

2 0 r 4.62 1011 F / m D ln o Di

C0 4.62 1011 80 3.7 109 F

2.1.1 Generators neutral are solidly grounded

Fig 2. Equivalent circuit for generators neutral are solidly grounded For solid grounded generators neutral, the current in the phase c (normal value) is much smaller than the short circuit current in phase a and b, to simply the calculation, Ic is assumed to be zero.

U ao U a U ao Z11 I a Z12 I b U bo U b U bo Z 21 I a Z 22 I b I 0 c The short circuit current in phase a and b

I a 15.44 69.9 kA I b 15.44129.9 kA

The induced voltage in phase c

U c U c 0 U c U c 0 Z31I a Z32 Ib 165.1129.6 kV

2.1.2 Generators neutral is isolated

3

Fig 3. Equivalent circuit for generators neutral is isolated

U ao U a U bo U b 0 Ic Ib I a U U I Z a c shunt U c 0 0 ao Z shunt 1 1 j 4223.3 7 j (C1 C0 C ) j 2 50(3.74 10 2 3.7 109 2 109 )

The short circuit current in phase a b and c

I a 15.2 60 kA I b 15.2120 kA I c 0.0085150 kA The induced voltage in phase c

U c U c 0 U c U c 0 Z31I a Z32 Ib 242.8 kV

2.2 Touch voltage

The expression of touch voltage is given by

V

I f 2

1 1 a x

For the short circuit current in case 2.1.1,

3800 15.44 103 1 1 1 1 V 9.3 103 kV 2 0.5 x 0.5 x Where x is the distance from feet to the tower, assume x=1, the touch voltage will reach 9300 kV.

4

2.3 Temperature increase of the power line

From the balance of the power, one can derive the relationship between the temperature rise and the current impulse in the certain time interval

W cv m I 2 Rdt cv md I 2...

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